Let's see... a couple of the ones I would've picked have been already mentioned, but here goes anyways.
Pan's Labyrinth: Yeah, the ending was very sad. But you want to know what really got me? Torturing the freaking stuttering guy. That was just going overboard. That scene was just painful to watch.
The Proposition: Again, another movie where the ending was really depressing, but by the time I got to that point, the events had left me so depressed I didn't care anymore. The mistreatment and then on-screen whipping to death of a mentally fragile teenage boy was just heartbreaking, despite the things he had been accused of doing prior to the movie's beginning.
Willard: I was reminded of this one by an above poster, but come to think of it, it really is one of the most depressing movies I've seen. Poor guy. D: However, while my sympathies were mostly directed towards him, what really did it was when his favorite rat Socrates died.
The End of Evangelion: Just.... poor Shinji. After having been the buttmonkey of the entire series, he's extremely depressed, almost killed, massively mindscrewed, and then left with, of all people, ASUKA, after the world's been destroyed? Again, poor guy.
Edward Scissorhands: One of the nicest characters, if not the nicest in the movie, is punished for things he doesn't realize are wrong, for doing what he sees as helping people he loves, by the very people who were friends with him when it was convenient for them, so much that he's driven away from his only chance at happiness. If that's not depressing, what is?
Come to think of it, any movie with an already awkward, out of place, put-upon individual getting stomped on until they die or just are left broken counts in my book.